Questions tagged [highest-density-region]
The smallest region over which a density exceeds a threshold. More useful for summarizing multimodal distributions than other probability regions. Frequently used in Bayesian statistics ("Highest Posterior Density Regions"). The term in one dimension is "Highest Density Interval".
10 questions with no upvoted or accepted answers
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Is there a theoretical motivation for how we construct confidence regions?
I've recently had to construct a confidence region for a vector of means $\theta \in \mathbb{R}^k$, and I realized my understanding of some concepts regarding the fundamentals of building confidence ...
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How to elicit prediction intervals from clients?
When I prepare probabilistic forecasts I am often left with a choice of what percentage highest-density region to choose for prediction intervals for clients. This matters for reporting uncertainty to ...
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How to compute a rectangular credible region from samples
Given high-dimensional Monte Carlo samples $\bf{X_1},...,\bf{X_N}$ from a probability distribution $p({\bf x})$ in $\mathbb{R^d}$, I want to estimate a rectangular highest-density credible region for $...
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How to determine the size of highest density region in high dimensions
I want to calculate the "size" of the highest density region (HDR) that contains p% of the total probability for multivariate samples of a Bayesian posterior obtained via MCMC.
In 1D this "size" is ...
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Can we generate HPD regions from MCMC draws using convex hulls?
I thought of a procedure to generate high probability density regions with probability $1-\alpha$ from $n$ MCMC draws:
Find the $\lfloor(1-\alpha)\cdot n\rfloor$ draws with the largest probability ...
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Extraction of modes from a multi-modal density function
I am trying to extract modes from a multi-modal density function and not just peaks. For example, in the two density functions below (images), I would like to extract the curves contained in the black ...
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When can a winner of the election be called: estimating population proportion without the assumption of random sampling
While following a recent election, I wanted to estimate population proportion of people who voted for a certain candidate knowing the sample proportion, sample size (and population size).
I first ...
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Find the CI for a given interval of HDI?
I'm working with big data that doesn't fit well to a distribution but often exhibits a peak (maybe two). I'm looking for a method to calculate the confidence for a given range around the mode.
For ...
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Bayesian hypotesis testing, can i use HPD?
I have a statistic question concerning the null hypotesis testing in bayesian inference.
I red that i can use HPD for testing the null value in a linear bayesian regression:
"We can then use the ...
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How is highest posterior density interval estimated in this code snippet?
I found the following (Julia) implementation for estimating the highest posterior density interval from a posterior sample (link). Below, I turn it into pseudocode for simplicity.
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